Problem:
Let be the set of points in the coordinate plane, where each of and may be -1,0 , or 1 . How many distinct lines pass through at least two members of ?
Answer Choices:
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Solution:
There are pairs of points in , and each pair determines a line. However, there are three horizontal, three vertical, and two diagonal lines that pass through three points of , and these lines are each determined by three di erent pairs of points in . Thus the number of distinct lines is . OR
There are 3 vertical lines, 3 horizontal lines, 3 each with slopes 1 and 1 , and 2 each with slopes , and , for a total of .
The problems on this page are the property of the MAA's American Mathematics Competitions